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Semiparametric Estimation of Conditional Quantiles for Time Series
Company: Technische Universitat Kaiserslautern
Year Of Publication: 2003
Month Of Publication: March
Pages: 153
Download Count: 877
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Comment Num: 0
Language: EN
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Who Can Read: Free
Date: 2-19-2005
Publisher: Administrator
Summary
The estimation of conditional quantiles has become an increasingly important issue ininsurance and financial risk management. The stylized facts of financial time series datahas rendered direct applications of extreme value theory methodologies, in the estimationof extreme conditional quantiles, inappropriate. On the other hand, quantile regressionbased procedures work well in nonextreme parts of a given data but breaks down inextreme probability levels. In order to solve this problem, we combine nonparametricregressions for time series and extreme value theory approaches in the estimation of extremeconditional quantiles for financial time series. To do so, a class of time series modelsthat is similar to nonparametric AR-(G)ARCH models but which does not depend on distributionaland moments assumptions, is introduced. We discuss estimation proceduresfor the nonextreme levels using the models and consider the estimates obtained by invertingconditional distribution estimators and by direct estimation using Koenker-Basset(1978) version for kernels. Under some regularity conditions, the asymptotic normalityand uniform convergence, with rates, of the conditional quantile estimator for ?-mixingtime series, are established. We study the estimation of scale function in the introducedmodels using similar procedures and show that under some regularity conditions, the scaleestimate is weakly consistent and asymptotically normal. The application of introducedmodels in the estimation of extreme conditional quantiles is achieved by augmenting themwith methods in extreme value theory. It is shown that the overal extreme conditionalquantiles estimator is consistent. A Monte Carlo study is carried out to illustrate thegood performance of the estimates and real data are used to demonstrate the estimationof Value-at-Risk and conditional expected shortfall in financial risk management and theirmultiperiod predictions discussed.
Author(s)
Mwita, Peter N. Sign in to follow this author
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